Occupational Choice, Human Capital, and Financial Constraints

by

Rui Castro and Pavel Ševčík

Working Paper # 2016-2 February 2016

Centre for Human Capital and Productivity (CHCP)

Working Paper Series

Department of Economics Social Science Centre Western University

London, Ontario, N6A 5C2 Canada

Occupational Choice, Human Capital, and

Financial Constraints∗

Rui Castro† Pavel Sevcık‡

February 2016 (latest version here)§

Comments Welcome

Abstract

We study the aggregate productivity effects of firm-level financial frictions. Credit

constraints affect not only production decisions but also household-level schooling de-

cisions. In turn, entrepreneurial schooling decisions impact firm-level productivities,

whose cross-sectional distribution becomes endogenous. In anticipation of future con-

straints, entrepreneurs under-invest in schooling. Frictions lower aggregate productiv-

ity because talent is misallocated across occupations, and capital misallocated across

firms. In addition, firm-level productivities are also lower due to distortions induced by

the schooling responses. We find that these effects combined account for about 1/5 of

the U.S.-India aggregate productivity difference. Requiring the model to match school-

ing differences significantly amplifies the impact of frictions, and the model accounts

for 58% of the aggregate productivity difference.

Keywords: Aggregate Productivity, Financial Frictions, Entrepreneurship, Human

Capital.

JEL Codes: E24, I25, J24, O11, O15, O16, 047.

∗We thank our discussants Pedro Amaral, Irineu de Carvalho Filho, and Diego Restuccia for extremelyhelpful comments, as well as seminar attendants at the 2013 CEA, 2013 SED, 2013 Lubramacro, 2013CMSG, 2014 Macroeconomics and Business CYCLE conference, 2015 Econometric Society World Congress,2015 Midwest Macro Conference, 20th Economics Day at Ensai, Bank of Canada, Kentucky, McGill, andPittsburgh. All errors are ours. Both authors acknowledge financial support from the SSHRC. Castroacknowledges financial support from the Fonds Marcel-Faribault/Universite de Montreal.†Department of Economics, University of Western Ontario. Email: rcastro7@uwo.ca. Web:

http://economics.uwo.ca/people/faculty/castro.html.‡Departement des sciences economiques and CIRPEE, ESG UQAM. Email: sevcik.pavel@uqam.ca. Web:

www.sevcik.uqam.ca.§First draft: June 2013.

1

1 Introduction

Total Factor Productivity (TFP) is the single most important factor accounting for the large

cross-country income differences we see in the data (Hsieh and Klenow, 2010; Caselli, 2005;

Hall and Jones, 1999; Klenow and Rodrıguez-Clare, 1997). We evaluate the role of financial

frictions as a source of TFP differences. The key friction is that entrepreneurs face a collateral

constraint when raising business capital. Our main contribution is to consider the role of

entrepreneurial schooling decisions, and how they interact with financial frictions.

We view entrepreneurial human capital as a main determinant of firm-level productiv-

ity. That is, more educated entrepreneurs are better managers, and therefore operate more

productive businesses. In this setting, future entrepreneurs under-invest in schooling in an-

ticipation of the presence of credit frictions. They do so because investing in schooling is

not very productive in small-sized firms, and also because the opportunity cost of schooling

investments is high when resources could be used instead to build up collateral. Intuitively,

entrepreneurs don’t invest much in education since they realize they will be running a small

family business; they prefer instead to work hard in order to save more. Further, schooling

investments get misallocated. That is, those entrepreneurs with the best productivity poten-

tial are the ones who feel compelled to reduce schooling investments the most. We find that

these two effects, schooling under-investment and schooling misallocation, play an important

quantitative role in accounting for the U.S.-India TFP differences.

Our model integrates two literatures/frameworks. One is a model of entrepreneurship

with credit constraints, along the lines of Buera and Shin (2013), Buera et al. (2011) and

Midrigan and Xu (2014), among others.1 The other is a model of human capital accumulation

along the lines of Erosa et al. (2010) and Manuelli and Seshadri (2014).

Like in the existing literature on entrepreneurship with credit constraints, financial fric-

tions generate a misallocation of talent into occupations. Namely, poor individuals talented

at entrepreneurship choose to become workers, since their firms would operate at an ineffi-

ciently small scale. Other individuals, not so talented at managing and operating a produc-

tion technology, find it advantageous to do so if sufficiently wealthy. Further, capital gets

1Other references include Castro et al. (2004, 2009), Erosa and Hidalgo-Cabrillana (2008), Amaral andQuintin (2010), Buera et al. (2011), Greenwood et al. (2013), Moll (2014), and Moll et al. (2014).

2

misallocated among those individuals that do decide to become entrepreneurs. This is be-

cause with credit constraints firm size depends on entrepreneurial wealth, not just firm-level

productivities. On top of these well-understood effects of credit constraints, our framework

generates additional ones, stemming from changes in entrepreneurial schooling choices and in

the distribution of firm-level productivities. A key feature of our setup is precisely that the

distribution of firm-level productivities becomes endogenous, determined by entrepreneurial-

level schooling decisions.

We quantify the role of these different effects of credit frictions on TFP. In line with the

previous literature, we first calibrate our model to the U.S. and consider a scenario where

the only fundamental difference between the U.S. and India is the overall degree of financial

frictions. In this case, our model accounts for about 1/5 of the U.S.-India TFP difference.

Capital misallocation is responsible for roughly half of this difference. The other half comes

mostly from the misallocation of entrepreneurial schooling investments. A second calibration

also lets the average productivity of the human capital accumulation technology vary across

the U.S. and India in order to match the average years of schooling differences across these

two countries. This results in a significant amplification of the effect of frictions, and in this

case the model is able to account for 58% of the TFP difference.

Our modelling of schooling decisions follows Erosa et al. (2010) and Manuelli and Seshadri

(2014). These papers emphasize the role of cross-country TFP differences. Our model shares

with these papers the feature that, in addition to time, expenditure in goods (or education

quality) is also a key input into the human capital accumulation process. As in these papers,

the education quality margin in our model leads workers to invest less in education in coun-

tries with lower wages (due to tighter credit frictions). In our paper, however, credit frictions

also discourage schooling investments among entrepreneurs, by reducing the marginal return

to those investments. The latter mechanism is independent from presence of an education

quality margin in the human capital accumulation process.2

Bhattacharya et al. (2013) also consider entrepreneurial investment in managerial skills, in

2There is an extensive literature on educational decisions under credit constraints. An early exampleis Galor and Zeira (1993), and more recent developments are in Lochner and Monge-Naranjo (2011) andCordoba and Ripoll (2013). As in these papers, credit constraints in our model act as a direct mechanismlowering education, namely among poorer individuals. However, the central role of credit constraints in ourmodel will be in affecting entrepreneurial, not worker, schooling decisions.

3

a setting with exogenously given distortions in firm size. As in their paper, the distribution of

firm-level productivities in our model arises endogenously from entrepreneurial investments in

human capital. In contrast to their framework, firm size distortions are endogenous here, and

depend on the wealth distribution. In our model, constrained entrepreneurs under-invest in

schooling in part in order to self-finance. This mitigates physical capital misallocation across

firms, a mechanism also emphasized by Midrigan and Xu (2014). Another difference is

that, in our model, human capital investments are also a determinant of occupational choice

decisions. The extent of under-investment in human capital by constrained entrepreneurs is

therefore bounded by their willingness to switch occupation.

Finally, our paper is also related to the resource misallocation literature, namely Restuccia

and Rogerson (2008), Hsieh and Klenow (2009), and Bartelsman et al. (2013). These authors

examine the aggregate productivity consequences of misallocation generated by firm-specific

taxes and subsidies. These taxes and subsidies are effectively stand-in, generic distortions,

meant to capture deeper allocative problems. Our model concentrates on one such allocative

problem: malfunctioning credit markets. We provide an explicit mapping between funda-

mental distortions coming out of our model, and the stand-in taxes and subsidies that are

typically considered in this literature. We also extend Hsieh and Klenow’s (2009) framework

for measuring the extent of resource misallocation. In our case, in addition to distortions to

cross-firm input allocation, there are also distortions to physical productivity relative to the

frictionless benchmark. The latter are induced by talent misallocation and by distortions to

entrepreneurial schooling investments. We find a significant quantitative role for the latter.

The paper is organized as follows. Section 2 describes the model. Section 3 analyzes the

optimality conditions. Section 4 describes the calibration procedure. Section 5 presents the

results, and Section 6 concludes. The Appendices contain detailed information about some

of the analytical properties of the model, the mapping between model and data, and the

numerical procedure.

4

2 Model

2.1 The Environment

Consider an economy with measure one of altruistic dynasties. Each individual lives for 2

periods, childhood and adulthood. The household, composed of a child and an adult parent,

is the decision unit, as if a household planner existed which pooled all household member

resources and coordinated all the decisions. We call childhood the period when schooling

and investment decisions are made, and adulthood the period when the individual’s main

economic activity is carried out.

Households value stochastic aggregate household consumption streams according to

E0

∞∑t=0

βtu (ct) . (1)

The period utility function u is of class C2, is strictly increasing, strictly concave, and satisfies

the usual Inada conditions.

In anticipation of our recursive formulation, we use primes to denote variables which

pertain to the next generation, whereas those without primes refer to the current one. The

household starts the period with wealth ω, and a draw of the child’s abilities, current learning

ability z and future entrepreneurial ability x. The inter-generational ability transmission is

governed by a first-order Markov chain with transition probabilities π (z′, x′|z, x).

Given the current state (ω, z, x), the household makes four decisions. First, it decides

today’s investment in the child’s education, by choosing years schooling s and schooling

expenditures e to produce human capital according to

h = z(sηe1−η)ξ , (2)

with η ∈ [0, 1] and ξ ∈ [0, 1).3 We follow Erosa et al. (2010) and Manuelli and Seshadri (2014)

3A more general formulation would be h = z(sηe1−η

)ξhζ0 + (1− µ) h0, where h0 is the child’s initial

human capital. Here we assume full depreciation (µ = 1), similarly to Erosa et al. (2010). The component

hζ0 is captured by mean learning ability in our specification. Intergenerational transmission of human capitalis therefore governed by the persistence in learning ability.

5

in considering private expenditures as an input to human capital accumulation in addition

to student time. This allows a worker’s schooling time to increase with wages. With the

presence of private expenditures, higher wages increase the marginal gain from schooling

investments by more than the marginal cost, since the price of the goods input is invariant

to the wage.4

Second, the household decides today’s saving for next period, by purchasing bonds in net

amount q at unit price 1/(1 + r).5 Third, it decides the child’s occupation for next period,

whether to become an entrepreneur or a worker. Workers supply their human capital at the

going wage rate. Entrepreneurs manage their own firms and are the residual claimants of

profits. Fourth, if the decision is to become an entrepreneur next period then the household

also needs to raise capital, possibly relying in part on external funds, and hire labor in order

to run the firm.

All production is carried out by entrepreneurs according to

y = xhθ(kαl1−α

)γ, (3)

with α, γ, θ ∈ (0, 1), where k and l denote physical capital and labor inputs. Entrepreneurial,

or firm-level productivity is given by xhθ, of which x is determined by luck, and h is the

accumulated human capital. Physical capital depreciates at rate δ ∈ (0, 1).

2.2 Household’s Problem

We focus on stationary equilibria, in which prices and the cross-sectional distribution over

individual states are time-invariant. Denote by w the wage rate (unit price of human capital)

and by r the real interest rate. We begin by formulating the household’s problem conditional

on the child’s occupational choice. It is convenient to consider the occupational choice before

4As in Erosa et al. (2010), this mechanism also relies on the presence of tuition costs, which we alsomodel. Tuition costs prevent the marginal gains and costs from an additional year of schooling to both varyproportionally with the current level of human capital, allowing schooling years to vary with both learningability z and, via school quality adjustments, wages.

5Given our assumption on the resolution of uncertainty, saving is contingent upon the child’s abilities,namely next period’s entrepreneurial ability. We abstract from precautionary saving behavior associated withentrepreneurial ability risk in order to streamline the analysis. This allows us to characterize the householdinvestment decisions via simple non-arbitrage conditions.

6

the remaining decisions. Since all uncertainty is resolved at the start of an individual’s life,

there is no loss in doing so.

Conditional on the child becoming a worker next period, the worker-household ’s problem

can be written recursively as:

vw (ω, z, x) = maxc,e,s,q

{u (c) + β

∑z′,x′

π (z′, x′|z, x) v (ω′, z′, x′)

}(Pw)

subject to (2) and

c+ wsl + e+1

1 + rq = wψh (1− s) + ω (4)

s ≤ s (5)

q ≥ −λφω (6)

ω′ ≡ wh+ q. (7)

Equation (4) is the budget constraint. The term wsl+ e is the direct cost of investing in the

child’s education, composed of tuition fees wsl (l is the total teacher input per unit of student

time, which is a parameter) and expenditures in education quality e. Teacher’s effective time

is not an input into human capital production, only student time is. Expenditures in goods

capture direct costs such as books and extracurricular activities. On the right-hand-side,

wψh (1− s) is the child’s labor earnings, where ψ ∈ (0, 1) captures increasing labor earnings

over an individual’s lifetime due to experience accumulation.

Equation (5) is the child’s time constraint (our assumptions on preferences and human

capital technology allow us to ignore the non-negativity constraints on consumption, time,

and schooling expenditures). We impose an upper bound s ≤ 1 for quantitative purposes,

to capture the fact that individuals do not normally spend their entire early life studying.

Households are subject to an inter-period borrowing constraint given by (6). They can

only borrow up to a multiple λφ ≥ 0 of their wealth.6 When φ = 0 no borrowing is

6This constraint can be motivated by a simple static limited enforcement problem. Suppose a householdborrows −q > 0 and then decides whether to default. The only penalty is that financial intermediariesmay seize a fraction ν ∈ [0, 1] of total wealth, including the amount just borrowed. Intermediaries thenrequire that the gain from defaulting does not exceed the cost, that is −(1 − ν)q ≤ νω. This yields (6)

7

allowed, and investment must be completely funded out of the household’s wealth; when

φ =∞ (provided λ > 0, which we assume below) access to credit is unconstrained. Finally,

equation (7) defines the initial wealth of the next household in the dynastic line, conditional

on the fact that next period’s parent will be a worker.

Similarly, conditional on the child becoming an entrepreneur next period, the entrepreneur-

household ’s problem reads:

ve (ω, z, x) = maxc,e,s,q

{u (c) + β

∑z′,x′

π (z′, x′|z, x) v (ω′, z′, x′)

}(Pe)

subject to (2), (4), (5), (6) and a new definition of household’s wealth which is now based

on entrepreneurial profits

ω′ ≡ Π (q, h, x) + q, (8)

where

Π (q, h, x) = maxk,l≥0

{xhθ

(kαl1−α

)γ − (r + δ) k − wl}

(Pf)

subject to

k ≤ λq, (9)

with λ ≥ 1. Entrepreneurs hire capital and labor to maximize profits, subject to an intra-

period capital constraint. The maximum level of capital an entrepreneur can use in pro-

duction is given by a multiple λ of the household’s second period wealth, which acts as

collateral.7 When λ = 1 no external funding is allowed, and capital is solely determined by

internal funds. When λ =∞ financial markets work perfectly, and capital is not constrained

by wealth.

with φλ ≡ ν/(1− ν) ≥ 0. The main advantage from using this simple specification is tractability. It shareswith self-enforcing limits based on dynamic incentives (Kehoe and Levine, 1993) the key feature that richerhouseholds are able to borrow more.

7We assume future profits are not pledgable as collateral. Constraint (9) therefore implies that householdsthat borrow today will not be able to run a firm tomorrow. As a result, only children from sufficiently wealthybackgrounds can aspire to become entrepreneurs. Similarly to (6), the constraint (9) may be motivated by asimple static limited enforcement problem. As in Buera and Shin (2013), suppose households borrow k fromfinancial intermediaries against collateral q, and then have a decision whether to default. The only penalty isthat intermediaries may seize the entire collateral, plus a fraction of κ of k. No default requires (1−κ)k ≤ q,which yields (9) with λ ≡ 1/(1 − κ) ≥ 1. Related work using identical collateral constraints include Evansand Jovanovic (1989), Moll (2014) and Moll et al. (2014).

8

Financial frictions affect the model via (6) and (9). The parameter λ governs the over-

all extent of financial frictions in the economy, including raising capital by entrepreneurs,

whereas φ is a parameter controlling the relative extent of consumer credit. We choose this

formulation to reflect the possibility that seizing wealth upon default, for example, might be

easier for one type of credit compared to the other. In our quantitative analysis we let λ

vary across countries while fixing φ.

We finally consider the household’s occupational choice for the child next period:

v (ω, z, x) = max {vw (ω, z, x, ) , ve (ω, z, x)} . (10)

2.3 Competitive Equilibrium

Definition. A stationary recursive competitive equilibrium is a set of value functions vw (ω, z, x),

ve (ω, z, x), and v (ω, z, x), together with the associated decision rules, a set of entrepreneurial

households B, prices w and r, and an invariant distribution over household states Ψ such

that given prices,

• vw (ω, z, x) and ve (ω, z, x) solve problems (Pw) and (Pe), respectively, and v (ω, z, x)

solves (10),

• the set of entrepreneur-households is defined by the optimal occupational choice rule:

B = {(ω, z, x) ∈ S | ve (ω, z, x) > vw (ω, z, x)} , (11)

where S ⊆ R× R2+ is the individual household’s state space,

• market for labor clears:

∫B

ldΨ +

∫S

sldΨ =

∫S\B

hdΨ +

∫S

(1− s)ψhdΨ, (12)

• market for capital clears: ∫B

kdΨ =

∫S

q

1 + rdΨ, (13)

9

• market for goods clears:

∫S

cdΨ +

∫S

edΨ + δ

∫B

kdΨ =

∫B

xhθ(kαl1−α

)γdΨ, (14)

• distribution Ψ is invariant:

Ψ(S)

=

∫S

P(X, S

)dΨ (X) for all S ∈ BS, (15)

where P : S × BS → [0, 1] is a transition function generated by the decision rules and

the stochastic processes for z and x, and BS is the Borel σ-algebra of subsets of S.

3 Analysis

In this section we present an analysis of individual optimal decisions. We start with en-

trepreneurial production decisions and proceed by backward induction to schooling and sav-

ings decisions. We finish with the occupational choice.

3.1 Production

Given their human capital, entrepreneurs hire labor and capital to maximize their prof-

its. The presence of the capital constraint implies that the profit function will differ for

constrained and unconstrained entrepreneurs:

Π (q, h, x) =

Π∗ (h, x) if q ≥ q∗ (h, x) (unconstrained)

Πc (q, h, x) else (constrained),

(16)

10

where

q∗ (h, x) = k∗/λ

k∗ =

[(1− α) (r + δ)1− 1

(1−α)γ

αw

](1−α) γ1−γ (

αγxhθ) 1

1−γ

l∗ =(1− α) (r + δ)

αwk∗

y∗ = xhθ((k∗)α (l∗)1−α)γ

Π∗ (h, x) = y∗ − wl∗ − (r + δ) k∗

≡ A(xhθ) 1

1−γ(17)

with A being a function of production function parameters and factor prices, and

kc = max {λq, 0}

lc =

[γ (1− α) (kc)αγ

wxhθ] 1

1−(1−α)γ

yc = xhθ((kc)α (lc)1−α)γ

Πc (q, h, x) = yc − wlc − (r + δ) kc

≡ B (q)(xhθ) 1

1−(1−α)γ − (r + δ)λq(18)

with B (q) also a function of production function parameters and factor prices, in addition

to saving.8 The constrained profit function is increasing in accumulated assets since higher

q allows the entrepreneur to raise more capital and increase the scale of the firm closer to its

optimal level.

3.2 Schooling/Saving Decisions

In our framework, schooling and savings are investments into two different assets (human

and physical capital). Our timing assumption allows us to characterize different investment

opportunities in terms of simple non-arbitrage equations that transpire from the first-order

optimality conditions for problems (Pw) and (Pe) with respect to s, e, and q. Financial

8 The expressions for A and B (q) can be found in Appendix A.

11

frictions will later on be represented as wedges distorting these conditions.

The first-order conditions read:9

−µ+ w

(l + ψh− ψ (1− s) ηξh

s

)u′ (c) = β

∑z′,x′

π (z′, x′|z, x) v1 (ω′, z′, x′)ω′2 (q, h, x) ηξh

s

(19)(1− wψ (1− s) (1− η) ξ

h

e

)u′ (c) = β

∑z′,x′

π (z′, x′|z, x) v1 (ω′, z′, x′)ω′2 (q, h, x) (1− η) ξh

e

(20)

−ν +1

1 + ru′ (c) = β

∑z′,x′

π (z′, x′|z, x) v1 (ω′, z′, x′)ω′1 (q, h, x) , (21)

where µ and ν are the Lagrange multipliers on the time constraint (5) and the borrowing

constraint (6), respectively. These equations apply conditional on either occupation, only the

partial derivatives of future wealth with respect to saving and human capital, respectively

ω′1 and ω′2, differ across worker and entrepreneur households.

Combining (19) and (20) allows us to obtain unconstrained schooling time as an implicit

function s(e, z, w) of schooling expenditures,

w(l + ψh

)=

η

1− ηe

s,

where s is strictly increasing in e. Schooling time is

s (e, z, w) = min {s(e, z, w), s} , (22)

yielding human capital

h(e, z, w) = z(s(e, z, w)ηe1−η)ξ . (23)

Combining (20), (21), and (23) gives us a non-arbitrage condition equating the returns to

9Notice that v1 is always defined at the optimum. Even though v has a kink in the wealth dimensioninduced by the occupational choice, the optimum will never occur at this kink. It follows that, at theoptimum, v1 is either equal to vw1 or to ve1. Notice also that, with sufficient smoothness introduced by theability shocks, which we assume, the first-order conditions are not only necessary but also sufficient for anoptimum. See Clausen and Strub (2013) for a formal discussion.

12

physical and human capital accumulation:

− ν + (1− η) ξh(e, z, w)

eω′2 (q, h (e, z, w) , x) = (1 + r) pe(h, s, e)ω

′1 (q, h (z, e) , x) , (24)

where for convenience we denote the shadow unit price of schooling expenditures to be

pe = pe(h, s, e) ≡ 1− wψ (1− s(e, z, w)) (1− η) ξh(e, z, w)

e, (25)

as it equals the unit of foregone consumption less the marginal increase in first-period earn-

ings, and ν ≡ ν (1 + r) pe/(β∑

z′,x′ π (z′, x′|z, x) v1 (ω′, z′, x′)). Specializing equation (24) for

each occupation allows us to characterize the optimal schooling decisions for worker and

entrepreneur households.10

3.2.1 Worker-Household

For a worker-household we have

ω′1 (q, h, x) = 1 and ω′2 (q, h, x) = w. (26)

As workers, all individuals have the same constant returns to human capital accumulation

since wages are linear in worker’s human capital. If the borrowing constraint does not

bind (q < −λφω and ν = 0), then we can substitute (26) in (24) and optimal schooling

expenditures solve:w

1 + r(1− η) ξ

h

e= pe, (27)

with h = h(e, z, w) and s = s(e, z, w). The left-hand-side is the discounted future benefit

of investing an extra unit of the final good on education, which is the wage rate times the

marginal increase in human capital. The right-hand-side is the marginal cost, which is the

unit of the good invested less the marginal increase in labor earnings enjoyed in the current

10A sufficient condition for the existence of an optimal solution is that θ1−γ (1− η)ξ < 1, which we assume

throughout. This condition always holds for worker households, who have linear returns on human capital(equivalent to setting θ = 1−γ in the condition). For entrepreneur households it is automatically satisfied if,for example, the entrepreneurial production function (3) has constant returns to scale in all variable inputs,i.e. θ = 1 − γ. Increasing returns are admissible as long as the human capital accumulation technologyexhibits sufficient curvature.

13

period.11

If instead the borrowing constraint binds (q = −λφω and ν > 0), then the worker-

household’s optimal expenditure solves:

maxe

{u

(ω − e− w

(sl − ψh (1− s)

)+

1

1 + rλφω

)+ β

∑z′,x′

π (z′, x′|z, x) v (wh− λφω, z′, x′)

}(28)

where s = s(e) and h = h(z, e) are given respectively by (22) and (23). In contrast to

the unconstrained case, the optimal schooling expenditures of a credit-constrained worker-

household depends on current wealth ω.

3.2.2 Entrepreneur-Household

The capital constraint (9), together with the condition that k ≥ 0, implies that entrepreneur-

households will always have q > 0 and therefore will never be credit-constrained. We have:

ω′1 (q, h, x) =

1 + ∂Πc

∂q(q, h, x) if q ∈ (0, q∗ (h, x)) ,

1 if q ≥ q∗ (h, x) ,

(29)

and

ω′2 (q, h, x) =

B (q) θαγ+1−γ

(xhθ) 1αγ+1−γ h−1 if q ∈ (0, q∗ (h, x)) ,

A θ1−γ

(xhθ) 1

1−γ h−1 if q ≥ q∗ (h, x) .

(30)

From (29) and (30) we can deduce how the marginal returns to physical and human capital

accumulation vary with the entrepreneur-household’s saving q. We obtain the following

result.

Proposition 1. Given h, capital-constrained entrepreneur-households (with q < q∗ (x, h))

face a higher marginal return to physical capital accumulation and a lower marginal return to

human capital accumulation than unconstrained entrepreneur-households (with q ≥ q∗ (x, h)).

11This condition also characterizes human capital investment decisions of unconstrained individuals (work-ers) in Erosa et al. (2010). Our paper draws attention to the impact of financial frictions on the educationdecisions of entrepreneur-households.

14

Proof. The first part of the proposition follows from (29), the fact that ∂Πc(q,h,x)∂q

is decreasing

in q, and that ∂Πc

∂q(q∗ (h, x) , h, x) = 0. The second part follows from (30), the fact that B (q)

is increasing in q, and that B (q∗ (h, x)) θαγ+1−γ

(xhθ) 1αγ+1−γ = A θ

1−γ

(xhθ) 1

1−γ .

The intuition behind the first part of Proposition 1 is that, for capital-constrained

entrepreneur-households, saving relaxes the capital constraint and allows them to expand

their firms closer to the optimal unconstrained scale. The second part holds because human

and physical capital are complementary in production. Capital-constrained entrepreneur-

households employ less capital, making their human capital less productive.

Proposition 1 shows how the capital constraint distorts saving and schooling decisions of

entrepreneur-households. These households have an incentive to save more and invest less

in education compared to unconstrained entrepreneur-households.

Substituting ω′1 and ω′2 for the case of q ≥ q∗ (h, x) into (24) yields the condition for

optimal schooling expenditures of capital-unconstrained entrepreneur-households:

A

1 + r(1− η) ξ

θ

1− γ

(xhθ) 1

1−γ

e= pe.

This condition is analogous to (27), with the left-hand side representing now the discounted

marginal increase in future profits from investing an additional unit of the final good on

schooling.

Analogously, we may replace ω′1 and ω′2 for the case of q ∈ (0, q∗ (h, x)) into (24) to obtain

the optimal schooling expenditures for capital-constrained entrepreneur-households:

B (q)

1 + r(1− η) ξ

θ

αγ + 1− γ

(xhθ) 1αγ+1−γ

e= pe

(1 +

∂Πc

∂q(q, h, x)

).

Compared to the unconstrained case, the marginal gain from investing in education is lower,

and decreasing returns set in faster (Proposition 1). The marginal cost is also higher, since

investing in education sacrifices wealth accumulation, which lowers firm capital and hence

profits. Optimal spending in education therefore depends on household wealth, via saving

q. Higher wealth helps relax the capital constraint, and reduces investment and schooling

15

distortions.

4 Calibration

We focus on the comparison between the U.S. and India. Our baseline strategy is similar

to Buera and Shin’s (2013), in the sense that we first calibrate the model economy to the

U.S. and then vary the financial friction λ, holding the remaining parameters constant, in

order to match India’s ratio of external finance to output. We call this the benchmark India

calibration.

We consider an alternative schooling calibration where we also allow the mean of the

learning ability distribution, z, to vary between the U.S and India, in order to match In-

dia’s average years of schooling. The purpose if this exercise is to ask how far we go in

accounting for the U.S.-India differences in production outcomes, namely TFP, assuming

we are able to account for schooling differences. We view cross-country differences in z as

representing differences in schooling quality not captured by current private expenditures.

These could be due to differences in public school quality, or differences in private or public

school infrastructure.

Our baseline parameters are described in Table 1. The first-order Markov chain governing

abilities is obtained from the discretization of a VAR(1) in logs where

ln (zt+1/z) = ρz (zt/z) + εzt+1,

ln (xt+1/x) = ρx (xt/x) + εxt+1,

and the disturbances are normally distributed with variance-covariance matrix

Σ =

σ2z σzx

σzx σ2x

.

We employ the procedure described by Tauchen and Hussey (1991), with 15 states for en-

trepreneurial ability and 4 states for learning ability.

We take one model period to be 30 years. Individuals start life at age 6. The period going

16

from age 6 until age 36 (childhood) is when schooling and early working in the labor market

take place. The period going from age 36 until retirement age 66 (adulthood) is when the

main economic activity, entrepreneurship or working for a wage, takes place.

Some parameters are calibrated externally to the model. These are in the top block of

Table 1. We normalize average entrepreneurial ability to 1. The coefficient of relative risk

aversion belongs to the interval of available estimates, and is a standard value in quantitative

analysis, as is the rate of physical capital depreciation. The parameters governing the income

share of capital (α) and the income share of entrepreneurial income (γ) are also standard

in models of entrepreneurship (see for example Atkeson and Kehoe, 2005, Restuccia and

Rogerson, 2008, and Buera and Shin, 2013).12 We set the autocorrelation coefficient of

learning ability to the intergenerational correlation coefficient of IQ scores reported by Bowles

and Gintis (2002), between the average parental IQ score and the average offspring IQ score.

Finally, we impose an upper bound on schooling time corresponding to 20 years of formal

schooling.

The remaining 14 parameters are chosen in order to minimize the sum of squared per-

centage deviations of 14 data moments from their model analogues. The bottom block of

Table 1 shows the values for these parameters, as well as the model’s success in matching

the data moments. As is common in this type of analysis, we identify each parameter with

a moment which we believe is particularly helpful in identifying it, although in the end all

parameters are jointly determined through a fairly complex system of nonlinear equations.

When computing the moments in the model, we take into consideration the overlapping

generations structure of our framework, and the fact that young household members split

their time endowment between formal schooling and work. Specifically, we assume a survey

protocol in our model in which agents report information only at the end of each model

period. In this case, individuals reporting to be workers in the model are all young household

members, irrespective of their future occupation, plus adult household members who chose

to work for a wage during the second period of their lives. Individuals reporting to be

12In our model with decreasing returns to scale income accrues to capital, labor, and the entrepreneurialinput. We attribute the latter to capital and labor incomes, in shares α and 1−α respectively. We thereforeequate α to the aggregate capital income share value.

17

Table 1: Benchmark calibration

Parameter Value Target Data Model

External calibration

σ 1.0 direct estimatesδ 0.844 yearly depreciation rate of 6%α 1/3 capital income sharex 1.0 normalizationγ 0.85 direct estimatesρz 0.72 intergenerational correlation of IQ scoress 2/3 up to 20 years of formal schooling (ages 6-26)

Internal calibration

β 0.215 yearly real interest rate 0.04 0.037z 51.6 average years of schooling among entrepreneurs 13.9 13.6ξ 0.85 average years of schooling among workers 13.7 14.2σz 0.09 earnings share of top 5% 0.35 0.32η 0.81 output share of schooling expenditures 0.045 0.047l 7.09 output share of teacher and staff compensation 0.05 0.046ψ 0.6 average labor earnings at age 46 over average at age 26 1.75 1.75θ 0.16 entrepreneurship rate 0.096 0.05ρx 0.45 intergenerational correlation of entrepreneurship 0.32 0.29σx 0.25 employment share of top 5% establishments 0.57 0.51σxz -0.1 ratio of median earnings (entrepreneurial over labor) 0.94 1.0φ 0.005 share of household credit in total external finance 0.19 0.21

λU.S. 9.22 ratio of external finance to output 2.91 2.25

λIndia 1.30 ratio of external finance to output 0.46 0.45

entrepreneurs are only adult household members who chose this occupation.13 We also take

one entrepreneurial firm in the model as corresponding to an establishment in the data.

We comment on each of the moments we have selected. A yearly real interest rate of 4%

is roughly between the real return on riskless bonds and the real return on equity over a long

horizon. Based on CPS (Current Population Survey) data, Levine and Rubinstein (2015)

report three relevant summary statistics: a rate of entrepreneurship (fraction of individuals

reporting to be self-employed) of 9.6%, average years of schooling of both entrepreneurs and

13For example, this implies that the rate of entrepreneurship in the model equals 1/2∫BdΨ, where the

division by 2 arises because, every period, each household is endowed with two time endowments of one uniteach.

18

workers around 14, and a ratio between the median annual earnings among entrepreneurs

to the median across workers of 0.9402.14 This moment is key at identifying a slightly nega-

tive covariance between innovations to learning and entrepreneurial abilities. Meaning that

households with high learning ability tend to have a slight disadvantage at entrepreneur-

ship. A higher covariance would imply a larger earnings ratio for entrepreneurs over workers

compared to the data.

For the output share of (public and private) schooling expenditures we use the same

number as Manuelli and Seshadri (2014), and for the output share of teacher and staff com-

pensation we use the same number as Erosa et al. (2010). The ratio of average labor earnings

at age 46 over the ratio at age 26 comes from Figure 1 of Kambourov and Manovskii (2009).

It is based upon the PSID (Panel Study of Income Dynamics) and refers to the cohort

entering the labor market in 1968. The intergenerational correlation of entrepreneurial occu-

pation is reported by Dunn and Holtz-Eakin (2000), and corresponds to the fraction of sons

of self-employed fathers in the NLS (National Longitudinal Surveys) who were themselves

self-employed at some point in the sample.

The employment share of the top 5% establishments is reported by Henly and Sanchez

(2009), based upon the U.S. Census County Business Pattern series. This figure is across

establishments in all sectors of activity in the year 2006. The number for the earnings share

of the top 5% comes from Dıaz-Gimenez et al. (2011) and is based on the Survey of Consumer

Finances.

The ratio of total external finance (including private credit) to output in the U.S. is

obtained from the 2013 update of the Beck et al. (2000) financial indicators database. We

adjust the reported stock market capitalization by the average book-to-market ratio, follow-

ing Buera et al. (2011). Our number is the average over the years 1990-2011. Our other

financial market indicator is the share of household credit in total external financing. We

obtained this value as the product between the share of household credit in total credit in

2005 from the International Monetary Fund (2006), and the share of total credit in total

external financing from the 2013 update of the Beck et al. (2000) data set, again averaged

14Levine and Rubinstein (2015) also report a ratio of average annual earnings between the two occupationsof 1.25, indicating a significantly more skewed earnings distribution among entrepreneurs. Our model isconsistent with this fact.

19

over the years 1990-2011.

Finally, in our schooling calibration we obtain λIndia = 1.27, and zIndia = 14.13, which is

about one quarter of the U.S. value. With these parameters, we are able to exactly match

India’s ratio of external finance to output of 0.46, and India’s average years of schooling of

5.26.

5 Results

5.1 Allocative Consequences of Financial Constraints

We begin with a qualitative analysis of the allocative effects of financial frictions. In the

absence of frictions, the wealth distribution should play no role in resource allocation, which

should depend only on the distribution of abilities. With financial frictions, the wealth

distribution interferes with resource allocation. We illustrate the different types of distortions

that arise in the model economy. We plot some of the model’s decision rules, for the U.S.

and India (benchmark calibration), at each time varying one of the states while holding the

remaining two constant. Our focus is on household-entrepreneurs.

5.1.1 Misallocation of Talent

The occupational choice is displayed in Figure 1. The left panel shows that low wealth

makes some ability types in India choose to become workers, whereas they engage in en-

trepreneurship in the U.S. This is because financial constraints are tighter in India. The

right panel shows that, both in the U.S. and in India, only individuals with sufficiently high

entrepreneurial ability become entrepreneurs. However, the entrepreneurial ability cutoff is

lower in India. Since input prices are lower in India (general equilibrium effect) this en-

courages some of the marginal ability types to become entrepreneurs. No selection effects

are evidenced in the middle panel for learning ability, an outcome which is specific to the

particular state we are looking at.

Figure 1 illustrates two forces underlying the misallocation of talent in the economy:

financial frictions discourage some good types from becoming entrepreneurs in India, whereas

20

105

!

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

occu

patio

n ch

oice

(1=

entr

epre

neur

ship

)

U.S.India

40 60 80

z

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

U.S.India

100

x

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

U.S.India

Figure 1: Entrepreneurship rate across ability and wealth

they encourage some bad types to engage in this activity. The resulting selection of types

into entrepreneurship is worse in India.

In net terms, the effect of attracting bad types into entrepreneurship dominates the effect

of discouraging good types, and the entrepreneurship rate is higher in India (6.5%) compared

to the U.S. (5%).

5.1.2 Production Distortions

Figure 2a displays the level of production depending on the current entrepreneurial state.

The left panel shows that, for sufficiently rich individuals, production is independent from

wealth. For them, production is higher in India because input prices are lower. Among

poorer individuals, instead, production declines with wealth. This happens at a faster rate

in India, where financial constraints are tighter. Tighter constraints lower production both

because firm size is lower, but also because firm-level productivity xhθ is lower. The latter

is due to the fact that entrepreneurs under-invest in education. For the very poorest, these

21

effects lead to output losses in India compared to the U.S.

The middle and right panels of Figure 2a show that, for given wealth, production in-

creases with both learning and entrepreneurial abilities. However, they increase at a faster

pace in the U.S. As ability levels increase, constraints become tighter, particularly in India.

When ability is higher, entrepreneurs in India are constrained to make more significant size

reductions relative to the optimum, and sacrifice schooling more, resulting in lower firm-level

productivity.

The behavior of capital-output ratios in Figure 2b is consistent with this discussion. Capi-

tal drops relative to output when entrepreneurs are constrained, which happens particulary in

India, and relatively poor and high-ability individuals. Absent financial constraints, capital-

output ratios should be independent from wealth, as well as from learning or entrepreneurial

ability.

Notice that endogenous schooling works to mitigate some of the effects of credit con-

straints on production. Although higher ability households do tend to be more credit-

constrained, in our model they are able to respond by sacrificing schooling investments.

This allows them to accumulate more wealth thereby relaxing credit constraints. Capital-

output ratios do not decline as much as they would otherwise, without schooling responses,

and production distortions tend to be lower.15 We illustrate these schooling responses next.

5.1.3 Investment Distortions

We display the saving and schooling expenditure decisions of entrepreneurs, as a function of

wealth, in Figure 3a. For sufficiently wealthy households, saving increases with wealth, and

is higher in the U.S. because of a higher interest rate. As wealth diminishes, at some point

the constraint on capital tomorrow will bind (the kink in the saving decision rule). This

arises earlier in India compared to the U.S., given tighter constraints in India. At this point,

in order to build more collateral, entrepreneurs save more today than they would normally

do.

The right panel of Figure 3a illustrates the under-investment in schooling by constrained

15This feature is related to Midrigan and Xu (2014), who emphasize the role of self-financing in mitigatingthe effect of credit frictions on capital misallocation. Our setup allows for self-financing to adjust to frictionsnot only through declines in current consumption, but also in schooling.

22

105

!

102

103

outp

ut (

y)

U.S.India

40 60 80

z

400

500

600

700

800

900

1000

U.S.India

2 4 6

x

103

104

U.S.India

(a) Production (y)

105

!

1.5

2

2.5

3

3.5

4

capi

tal-o

utpu

t (k/

y)

U.S.India

40 60 80

z

1.6

1.8

2

2.2

2.4

2.6

2.8

U.S.India

2 4 6

x

100

U.S.India

(b) Capital-output ratios (k/y)

Figure 2: Production and capital-output ratios across ability and wealth

entrepreneurs. In sufficiently wealthy households, schooling depends only on learning and

entrepreneurial abilities, not on wealth. Expenditure levels are higher in India, once again

23

102 104

!

100

101

102

103

104

savi

ng (

q) o

f ent

repr

eneu

rs

U.S.India

102 104

!

100

101

scho

olin

g ex

pend

iture

s (e

) of

ent

repr

eneu

rs

U.S.India

(a) Saving and schooling against wealth

40 60 80

z

12

14

16

18

20

22

24

26

28

30

32

savi

ng (

q) o

f ent

repr

eneu

rs

U.S.India

40 60 80

z

2.5

3

3.5

4

4.5

5

scho

olin

g ex

pend

iture

s (e

) of

ent

repr

eneu

rs

U.S.India

(b) Saving and schooling against learning ability

Figure 3: Saving and schooling expenditures of entrepreneurs

because of lower input prices: optimal firm size is higher in India for these individuals,

increasing the marginal return to education. Among poorer households, however, schooling

24

declines with wealth. This happens both because of a lower marginal return to schooling

investments, and a higher opportunity cost. Constrained entrepreneurs would rather build

collateral than spend on education.

Figure 3b gives some further indication of how financial frictions distort saving and school-

ing decisions. Both in the U.S. and in India, schooling increases with learning ability. How-

ever, the slope of the profile is higher in the U.S. In this country, as learning ability increases,

entrepreneurs are willing to cut back on saving and devote more resources to schooling, see

right panel of Figure 3b. Not the case in India, where higher learning ability also means a

tighter constraint on firm size, leading entrepreneurs not only to increase schooling expen-

ditures by less, but also to actually increase saving. All of this in an attempt to build more

collateral for the next period and relax frictions.

5.2 Measuring Misallocation

We rely on the framework of Hsieh and Klenow (2009) to gauge the extent of misallocation

in our model. That is, we will capture the extent of model-driven production and investment

distortions by means of generic distortions affecting a simple stand-in firm decision problem.

In broad terms, our strategy follows in two steps. First, we show that the generic pro-

duction distortions considered by Hsieh and Klenow (2009) do have a specific interpretation

in terms of our model. Second, we use and extend Hsieh and Klenow’s (2009) framework to

decompose the extent of model-based TFP differences in terms of average firm-level produc-

tivity and input misallocation effects.

Hsieh and Klenow (2009) focus on revenue productivity (TFPR) as a measurement tool,

following Foster et al. (2008). This notion of total factor productivity is obtained by dividing

nominal production revenue by an appropriate measure of production inputs. As Hsieh

and Klenow (2009) show, the distribution of TFPR across production units is particularly

informative about misallocation. In the benchmark case of no frictions, this distribution

is degenerate, as TFPR reflects only factors which are common across production units,

such as market prices and common technological parameters. Importantly, TFPR does not

reflect differences in real, or physical productivity across units (TFPQ in the literature’s

terminology), it only reflects unit-specific deviations from marginal product equalization. As

25

we shall show, under some conditions a more dispersed TFPR distribution is associated with

a higher the degree of misallocation frictions. A more dispersed TFPR distribution indicates

larger TFP gains may be obtained by reallocating the existing aggregate level of production

inputs away from low and towards high TFPR firms.

Our first goal is precisely to compute model-based distributions of TFPQ and TFPR in

order to characterize firm-level productivity and input misallocation effects in the production

sector. Our approach provides an explicit mapping between TFPQ and TFPR, and deeper

financial frictions.

5.2.1 Basic Model Wedges

Financial frictions distort decisions by introducing what amounts to individual-level wedges

in the optimality conditions that would emerge in the frictionless case. We call them basic

distortions, or basic model wedges. We first identify these basic wedges, and then show

how they map into proxy, or stand-in misallocation wedges. The latter are generic wedges

featured in much of the misallocation literature, for example Restuccia and Rogerson (2008),

Hsieh and Klenow (2009) and Bartelsman et al. (2013), among many others. Since our focus

is on production distortions, we shall concentrate on entrepreneur-households.

The entrepreneur-household’s optimality conditions under frictions (Section 3.2) can be

re-written as their counterpart absent frictions, distorted by two basic individual-level wedges

which we label τ eq and τ eh:

u′ (c) = β (1 + r)(1 + τ eq

)∑z′,x′

π (z′, x′|z, x) v1 (ω′, z′, x′) , (31)

peu′ (c) = β (1− η) ξ (1− τ eh)

θ

1− γA

(xhθ) 1

1−γ

e

∑z′,x′

π (z′, x′|z, x) v1 (ω′, z′, x′) . (32)

These equations define two basic wedges for the entrepreneur-household as a function of

the current state. These wedges capture distortions to the marginal value of future wealth

of additional saving and human capital levels due to the presence of financial constraints,

as described by (29) and (30). They replicate the optimality conditions (20) and (21) for

26

constrained entrepreneurs provided that

τ eq =

∂Πc (q, h, x) /∂q if q ∈ (0, q∗ (h, x)),

0 if q ≥ q∗ (h, x),

τ eh =

1− B(q)A

1−γαγ+1−γ

(xhθ)− αγ

(1−γ)(αγ+1−γ) if q ∈ (0, q∗ (h, x)),

0 if q ≥ q∗ (h, x).

The wedge τ eq ≥ 0 acts like a subsidy to saving, capturing the fact that whenever the

capital constraint binds, an increase in saving today relaxes the constraint and increases

profits tomorrow. That is, for constrained entrepreneurs, ∂Πc

∂q(q, h, x) > 0.

The wedge τ eh ∈ [0, 1] acts like a tax on the returns to schooling, capturing the fact that

human capital is less productive for constrained entrepreneurs. This is because physical

capital is lower, and complementary to human capital.

Notice that, relative to the economy without frictions, individual decisions in the econ-

omy with frictions are affected not only by the presence of distortions but also by general

equilibrium price effects.

5.2.2 Production Wedges

We now recast the firm’s problem as in Hsieh and Klenow (2009). We call it the proxy firm

problem:

Π = maxk,l≥0

{(1− τa) px (h∗)θ

(kαl1−α

)γ − (1 + τk) (r + δ) k − wl}, (Pf′)

where h∗ is the human capital level that would emerge absent financial frictions (but still

subject to the prices under frictions), and p is the output price, which may be normalized to

1 in our setup.

We label τa and τk individual-level proxy wedges, in the sense that they are generic wedges

standing-in for the fundamental distortions affecting the economy. τa captures distortions

along the potential revenue (i.e. revenue based on potential productivity x(h∗)θ) vs cost

margin, whereas τk captures distortions along the capital vs labor input cost margin. Our

task is now to infer proxy wedges from basic wedges. The proxy firm problem (Pf′) yields

27

the same solution as the original firm problem (Pf) when

1− τa =

(h

h∗

)θ1 + τk = 1 +

ζ

r + δ,

where ζ is the multiplier on the capital constraint.

It is possible to uncover an explicit mapping between proxy and basic distortions. Ap-

plying the Envelope theorem and using the definition of τ eq :

1 + τk = 1 +τ eq

λ (r + δ).

A mapping between τa and basic distortions obtains in closed form when ψ = 0. In this

case pe = 1 and, further assuming that the time constraint is slack, optimal schooling time

s is proportional to expenditures e. Combining (31) and (32) under the constrained and the

unconstrained cases, we obtain

1− τa =

(1− τ eh1 + τ eq

) θξ

1− ξθ1−γ ,

where ξθ < 1− γ given our parametric assumptions.

These expressions allow us to interpret the two proxy wedges in terms of our financial

frictions model. First, τk ≥ 0 amounts to a tax on capital. The reason is that the capital

constraint increases the shadow rental price of capital. Second, τa ∈ [0, 1] amounts to a

reduction in a firm’s physical output. The reason is that the capital constraint decreases

actual firm-level productivity xhθ below potential, by discouraging entrepreneurial school-

ing investments. The total disincentive to investing in human capital is captured by the

composite distortion (1− τ eh)/(1 + τ eq ). This composite distortion amounts to a positive tax

since (i) capital-constrained entrepreneurs run smaller firms, reducing the returns to invest-

ing in human capital, and (ii) for these households, accumulating wealth relaxes the capital

constraint, and therefore commands a higher return compared to investing in human capital.

An alternative parametric case useful considering is for l = 0 (and ψ > 0), assuming

28

again a slack time constraint. We obtain

1− τa =

(1− τ eh1 + τ eq

) 1−(θ−η)ξθξ(1−γ)

(p∗epe

) 1−(θ−η)ξθξ(1−γ)

, (33)

where p∗e is the shadow unit price of schooling expenditures ignoring credit constraints.

Although a closed form is not available, this formulation illustrates the role of schooling

expenditure prices in amplifying the effect of the composite distortion on τa, especially for

individuals with low learning ability z, or in countries with low z. Recall from (25) that pe

equals one unit of the final good net of the increase in first-period earnings afforded by the

additional human capital. Individuals with lower first-period earnings (lower z) tend to have

higher pe, and especially higher p∗e. The higher p∗e/pe faced by these individuals captures

the fact that schooling investments are particularly expensive for them, as they are less

productive in generating first-period resources potentially available for building up collateral

for the second-period entrepreneurial activity. This amplification mechanism is present in

our general formulation, and will play a key role when comparing economies with different

z.

The production technology underlying the stand-in problem (Pf′) is y ≡

(1− τa)x (h∗)θ (kαl1−α)γ. We follow Hsieh and Klenow (2009) in defining a firm’s (actual)

physical productivity TFPQ and revenue productivity TFPR as16

TFPQ ≡ y

(kαl1−α)γ= (1− τa)x (h∗)θ

TFPR ≡ py

kαl1−α.

16Notice that although the wedge τa looks similar to the revenue distortion τy of Hsieh and Klenow (2009),it plays a different role in our setting. Unlike τy in Hsieh and Klenow (2009), τa is a wedge between potentialand actual physical productivity. It does not act as a pure revenue tax, representing instead the physicalproductivity effects of lower schooling investments. For this reason, τa is part of the definition of TFPQ,whereas τy would be part of the definition of TFPR, as in Hsieh and Klenow (2009). In terms of our model,in fact, there are no revenue distortions as defined by Hsieh and Klenow (2009).

29

The optimality conditions are

γ(1− α)

(k

l

)αTFPR = w

γα

(k

l

)α−1

TFPR = (1 + τk) (r + δ) ,

and sok

l=

α

1− αw

(1 + τk) (r + δ).

Revenue productivity is therefore

TFPR ∝ (1 + τk)α .

Absent frictions, τ eq = τ eh = 0 and e = e∗. Therefore τa = τk = 0. In this case the

distribution of TFPR is degenerate, and the distribution of TFPQ reflects only individual

heterogeneity in abilities among households selecting into entrepreneurship. With frictions,

we expect the distribution of TFPR to become more dispersed, reflecting greater physical

capital misallocation, and the distribution of TFPQ to shift to the left, reflecting lower levels

of entrepreneurial human capital for constrained entrepreneurs.

Figure 4 plots the distributions of TFPR and TFPQ in our model, for both the U.S. and

the India (benchmark) calibrations. The degree of production misallocation in the economy

with frictions is large. The standard deviation of log TFPR more than doubles from the

U.S. to India. The mean of the TFPQ distribution is 10% smaller in India, and is also more

dispersed.

The next section will provide an explicit link between aggregate productivity and the

moments of the TFPR and TFPQ distributions.

5.3 Misallocation and Aggregate Productivity

The final good sector admits an aggregate production function in our setting (see Appendix

B):

Y = TFP(KαL1−α)γ ,

30

s.d. = 0.092

010

2030

4050

6070

80Pe

rcen

t

1/2 1 2 4TFPR relative to mean (log)

mean = 3.8

s.d.(log) = 0.307

010

2030

4050

60Pe

rcen

t

2 4 6 8 10 12 141618TFPQ

(a) TFPR and TFPQ in the U.S.

s.d. = 0.270

010

2030

4050

6070

80Pe

rcen

t

1/2 1 2 4TFPR relative to mean (log)

mean = 3.27

s.d.(log) = 0.369

010

2030

4050

60Pe

rcen

t

2 4 6 8 10 12 141618TFPQ

(b) TFPR and TFPQ in India

Figure 4: Revenue and physical productivity distributions

where Y ≡∫BydΨ, K ≡

∫BkdΨ, and L ≡

∫BldΨ, and total factor productivity (TFP) is

an aggregator of individual physical productivities and distortions

TFP ≡

∫B

(x (h∗)θ 1−τa

(1+τk)αγ

) 11−γ

dΨ[∫B

(x (h∗)θ 1−τa

(1+τk)1−γ+αγ

) 11−γ

dΨ

]αγ [∫B

(x (h∗)θ 1−τa

(1+τk)αγ

) 11−γ

dΨ

](1−α)γ.

Defining

TFPR′ ≡ TFPR (1 + τk)α(γ−1) ∝ (1 + τk)

αγ

we can rewrite aggregate TFP as

TFP =

∫B

(TFPQ

TFPR′

TFPR′

) 11−γ

dΨ, (34)

where TFPR′

is a geometric average of average marginal products of capital and labor.17,18

17The presence of decreasing returns to scale in production (γ < 1) introduces a slight difference betweenTFPR and the weights on TFPQ in the expression for TFP , which we define as TFPR′. The two quantitiesbehave very similarly though.

18TFPR′ ≡

{[∫B

(TFPQTFPR′

) 11−γ 1

1+τkdΨ

]α [∫B

(TFPQTFPR′

) 11−γ

dΨ

]1−α}γ(1−γ)κ1−γ , with

31

Expression (34) is identical to the one obtained in Hsieh and Klenow’s (2009) accounting

framework. We extend their framework by considering distortions impacting firm-level phys-

ical productivity (τa).

To better understand the impact of distortions on aggregate TFP it is instructive to

consider the case in which x (h∗)θ, (1− τa), and (1 + τk) are jointly log-normally distributed

among firms. The logarithm of aggregate TFP can then be written as a function of a few

key moments of the joint distribution of firm-level wedges and potential productivities:

log TFP = (1− γ) log ent+(1− γ) log EB

[TFPQ

11−γ

]−1

2

αγ (1− γ + αγ)

1− γvarB (log TFPR) ,

(35)

where ent ≡∫B

1 dΨ is the measure of the set of entrepreneur-households, and the expecta-

tion and the variance are conditional on the states in this set.

This expression is very similar to the one obtained by Hsieh and Klenow (2009), their

equation (16), with two differences. First, since γ = 1 in their baseline case, the first term

is absent. Second, and more importantly, in their case the TFPQ distribution is exogenous.

Here it is itself a function of the degree of financial frictions, through the response of schooling

investments. This response entails an amplification of the aggregate productivity effects of

financial frictions, which go beyond capital misallocation.

The first term in equation (35) is the TFP gain from specialization. Since firm-level

technology exhibits decreasing returns to scale, aggregate productivity rises when output

is produced by a larger number of smaller firms. The other two terms in equation (35) il-

lustrate two channels through which firm-level distortions reduce the aggregate TFP. First,

τa decreases the average firm-level physical productivity, by introducing a gap between po-

tential actual (TFPQ) and potential physical productivities (x (h∗)θ). This effect is due to

lower human capital investments by the entrepreneur-households in face of financial frictions.

Second, dispersion in τk reduces aggregate TFP by introducing dispersion in marginal prod-

ucts of capital across firms, which is the effect traditionally emphasized by the misallocation

literature.19

κ ≡ 1γ

(w

1−α

)1−α (r+δα

)α.

19Notice that, unlike TFPQ, the average level of TFPR does not impact TFP . Intuitively, if all firmshave the same gap between input prices and marginal products, aggregate productivity won’t increase by

32

Decomposing further the second term in equation (35) allows us to identify five key

moments that determine the total effect of financial frictions on aggregate TFP

log TFP = (1− γ) log ent︸ ︷︷ ︸Specialization

+ (1− γ) log EB

[x (h∗)

θ1−γ

]︸ ︷︷ ︸

Potential productivity

+ (1− γ) log EB

[(1− τa)

11−γ

]︸ ︷︷ ︸

Schooling under-investment

+1

1− γcovB

(log(x (h∗)θ

), log (1− τa)

)︸ ︷︷ ︸

Schooling misallocation

− 1

2

αγ (1− γ + αγ)

1− γvarB (log (1 + τk))︸ ︷︷ ︸

Capital misallocation

.

(36)

The first and the last terms are once more the specialization gain and physical capital

misallocation effects. The total effect on firm-level productivity EB

[TFPQ

11−γ

]is now de-

composed into three components. The potential productivity term is determined by the

selection of households into entrepreneurship, and thus by the misallocation of talent. In

addition, it also reflects changes in entrepreneurial human capital investment due to changes

in prices. The schooling under-investment term represents the effect of financial frictions

on entrepreneur-household investments in human capital. As this term shows, the average

level of schooling distortions τa matters for aggregate TFP.20 The schooling misallocation

term stems from the interaction between selection into entrepreneurship and human capital

investments of entrepreneur-households. A negative covariance between x (h∗)θ and (1− τa)

decreases aggregate TFP, since in this case entrepreneurs with the highest potential firm-level

productivities face the largest distortions. In other words, the most talented entrepreneurs

face the largest disincentive to invest in schooling, and therefore experience the largest pro-

ductivity declines relative to potential.

5.4 Aggregate Consequences of Financial Frictions

We now consider the aggregate consequences of frictions in the model, for the U.S. and the

two India calibrations, benchmark (when only λ differs from the U.S.) and schooling (when

reallocating a given level of aggregate capital across firms.20This contrasts with Hsieh and Klenow’s (2009) framework, where only the dispersion and not the level of

(revenue plus capital) distortions matters for aggregate TFP, to the extent that dispersion in wedges inducesdispersion in marginal products.

33

also z differs, in order to match average years of schooling in India). Table 2 looks at the

implications for aggregate output, capital-output ratios, and aggregate TFP, both in the

model and in the data. Our data source is version 8.1 of the Penn World Tables (Feenstra

et al., 2013). Appendix C describes in detail the mapping of the aggregate production

function between model and data.

Y K/Y TFP

Model Data Model Data Model Data

U.S. 1.00 1.00 2.21 2.99 1.00 1.00

India - bench 0.800.08

1.871.93

0.840.26

- school 0.07 1.95 0.57

Table 2: Macroeconomic aggregates

The model produces significant differences in these macroeconomic aggregates. The mag-

nitudes are smaller than what we see in the data for the benchmark (‘bench’) calibration, but

very close for the schooling (‘school’) calibration. Namely, under the benchmark calibration,

the model accounts for 22% of the 74 percent India-U.S. TFP difference, and for 22% of the

92 percent aggregate output difference. Under the schooling calibration, it accounts for 58%

of the TFP difference, and generates an output difference as large as in the data.21

Table 3 provides a decomposition of the TFP difference in line with equation (36). As

discussed previously, this decomposition is valid under a joint log-normality assumption.

This appears to be a good approximation, based on the fact that, as the bottom of Table 3

shows, the actual TFP difference (from Table 2) are reasonably close to the TFP difference

implied by equation (36).

According to this decomposition, the specialization term contributes negatively to the

U.S.-India TFP difference, since the entrepreneurship rate is higher in India. The other two

terms, firm-level productivity and physical capital misallocation, contribute each to about a

10% TFP difference under the benchmark calibration. The contribution of firm-level pro-

ductivity is further decomposed into three terms. Potential productivity is on average higher

21The reason the latter calibration delivers output differences in line with the data in spite of lower TFPdifferences is that human capital stock differences turn out to be larger than the PWT8.1 estimates we relyupon to compute TFP - see Appendix C - even if we do match average schooling years differences.

34

in India, since input prices are lower, in spite of a worse ability selection into entrepreneur-

ship. Lower input prices give incentives for unconstrained entrepreneurs to expand further

their production scale, and hence invest more in education. A lower interest also encourages

entrepreneurs to invest more in education, for given production scale. This term therefore

contributes negatively to the model’s U.S.-India TFP difference. However, schooling under-

investment is more important in India, contributing to a 5.2% loss in TFP relative to the

U.S. Finally, there is also a significantly higher degree of schooling misallocation in India

compared to the U.S. The most talented entrepreneurs in India are the ones cutting back

the most in terms of education, and this effect entails a 4% TFP loss.

The firm-level productivity effect is significantly larger under the schooling calibration,

accounting in this case for a 46% TFP loss in India. One of the main effects, not surpris-

ingly, comes from what is now a 22% loss in potential productivity. This is due to the

direct productivity effect of a lower z, compounded by lower schooling investments absent

frictions. The most interesting outcome is that frictions now play a much more significant

role. Schooling under-investment contributes to a TFP loss which is more than twice as

large, and schooling misallocation now entails a 21% TFP loss compared to the U.S.

The intuition behind these larger effects can be traced back to the discussion surround-

ing (33). The productivity of human capital investments in India is on average lower under

the schooling calibration. This effectively weakens the self-financing channel for future en-

trepreneurs, by lowering their first-period wage earnings. For given basic distortions, stem-

ming from the presence of financial frictions, a lower ability to raise first-period earnings

makes schooling investments more expensive. This mechanism amplifies schooling under-

investments in India, and generates individual-level productivity distortions τa which are

higher on average, as well as more dispersed across individuals.

Table 4 focuses on a few key micro-level features underlying production. It displays the

rate of entrepreneurship and the average firm size (relative to the U.S).

The rate of entrepreneurship in the U.S. comes again from Levine and Rubinstein (2015),

see Section 4. For India, we rely on the information provided in Table 6 of Mitra and Verick

(2013). They report a rate of self-employment for males aged 15-59 ranging from 41 percent

in urban settings to 53 percent in rural settings (years 2009-10). We focus on the average of

35

TFP term % Loss India relative to U.S.bench school

Specialization –0.072 –0.076Firm-level productivity +0.093 +0.463

Potential productivity –0.004 +0.222Schooling under-investment +0.052 +0.131Schooling misallocation +0.039 +0.206

Physical capital misallocation +0.103 +0.092

Approximate TFP 0.127 0.476

Actual TFP 0.161 0.428

Table 3: Aggregate TFP loss decomposition

the two.

U.S.

India

0.2

.4.6

.81

Cum

ulat

ive

Frac

tion

Empl

oyee

s

.5 .6 .7 .8 .9 1Cumulative Fraction Establishments

Figure 5: Lorenz curves, model (straight line) vs data (dotted line)

In the data, our measure of size is the number of employees.22 Once again, we take the

data counterpart of an entrepreneurial firm in the model to be an establishment. For the

U.S., the evidence comes from Henly and Sanchez (2009), based on the Census Bureau’s 2006

County Business Pattern Series. They report an average of 15 employees per establishment

22We use the total firm-level labor input as the model counterpart. Unfortunately our model does notdistinguish between the number of workers and the quantity of human capital employed. To partially addressthis issue, we equate the number of workers employed by a firm to l/hw, where hw is the average level ofhuman capital per worker in the whole economy.

36

ent.rate avg. firm size

Model Data Model Data

U.S. 0.050 0.096 1.00 1.00

India - bench 0.0800.470

0.730.29

- school 0.082 0.16

Table 4: Entrepreneurship rate and average firm size

across all sectors of activity (their Figure 1). For India, we rely on the Fifth Economic Census

by the Indian Ministry of Statistics and Program Implementation, which concerns the year

2015.23 The data is available for all sectors of activity across all Indian states, in both urban

and rural settings. It provides the same type of information (i.e. establishment and worker

counts by establishment size groups) as the County Business Pattern Series in the U.S. This

allows us to apply the same method as Henly and Sanchez (2009) to obtain approximations

to the relevant moments of the size distribution in India from the establishment and worker

counts, and ensures comparability across the two countries.24 We obtain an average of 4.38

employees per establishment in India, which implies a India-U.S. ratio of 0.29 in the data.

Consistently with the data, our model generates more entrepreneurs in India, operating on

average at a smaller scale. The main mechanism driving the higher rate of entrepreneurship is

the drop in input prices, which encourages lower ability individuals to engage in production.

The magnitude is much lower than the one we obtain from the data.

The establishment-size distribution, both in the model and in the data, not only gets

shifted to the left in India, but also develops a more pronounced right skew: there is a

larger mass of very small firms in India. This pattern is illustrated in Figure 5 for the

benchmark calibration.25 As in the data, the smaller firms in India account for a larger

fraction of aggregate employment compared to the U.S. Overall, the model delivers firm-

size distribution differences which are consistent with the data, however the magnitudes

are smaller in the model. The model accounts for about one half of the 2/3 India-U.S.

23Freely available at http://mospi.nic.in.24The mean establishment size can be calculated exactly from the establishment and worker counts. Higher-

order moments can be approximated by assuming a triangular distribution for the establishments inside eachsize group. See Henly and Sanchez (2009).

25The Lorenz curves under the schooling calibration are qualitatively similar, however the gap betweenmodel and data is larger.

37

aggregate workers entrepreneurs

Model Data Model Data Model Data

U.S. 14.16 13.70 14.21 13.70 13.60 13.90

India - bench 13.595.26

13.61–

13.41–

- school 5.26 5.41 3.61

Table 5: Schooling

difference in average firm size under the benchmark calibration, which gets overstated under

the schooling calibration.

Table 5 looks at average years of schooling. The U.S. data, both aggregate and by

occupation, are averages over 1996-2012 from the Current Population Survey as reported

by Levine and Rubinstein (2015). The Indian data is unfortunately only available for the

aggregate, and comes from Barro and Lee (2013). We use the reported average years of

schooling of the population older than 15 years over 1995-2010.

The model produces lower schooling levels in India independent of occupation, however

the magnitude is significantly lower than in the data under the benchmark calibration. One

reason the model is unable to deliver a larger effect is that the interest rate is lower in India,

which gives incentive for larger schooling investments in this country both among workers

and entrepreneurs.

The schooling calibration matches the average years of schooling in India by design, and

therefore produces much larger schooling responses across occupations as well. The effect is

more pronounced across entrepreneurs, highlighting the central mechanism of our model.

6 Concluding Remarks

We investigate the aggregate productivity effects of financial frictions, in an environment

where frictions impact both firm-level investment decisions, and household-level schooling

decisions. We show that, in anticipation of the effect credit constraints have on their future

business activity, entrepreneurs under-invest in schooling. Further, this behavior is more

pronounced among the most able entrepreneurs, generating a misallocation of schooling

investments. Both effects are shown to produce important aggregate productivity losses.

38

We are able to account for about 1/5 of the U.S.-India aggregate productivity difference,

of which half is due to these effects. A calibration that matches the U.S.-India difference

in average years of schooling significantly amplifies the impact of financial frictions. In this

case the model accounts for 58% of the TFP differences.

39

A Profit Functions

The profit functions are:

Π∗ (h, x) = A(xhθ) 1

1−γ ,

Πc (q, h, x) = B (q)(xhθ) 1

1−(1−α)γ − (r + δ)λq,

where

A =

[A0

((1− α) (r + δ)

αw

)1−α]γ

(1− γ) ,

A0 =

[(1− α) (r + δ)1− 1

(1−α)γ

αw

](1−α) γ1−γ

(αγ)1

1−γ ,

B (q) = B0 (qαγ)1

1−(1−α)γ ,

B0 =1− (1− α) γ

(1− α) γw

[(1− α) γλαγ

w

] 11−(1−α)γ

.

B Aggregation

The individual input demands from problem (Pf′) can be written as

l =

[x (h∗)θ 1−τa

(1+τk)αγ

] 11−γ

∫B

[x (h∗)θ 1−τa

(1+τk)αγ

] 11−γ

dΨ

L ≡ $lL

k =

[x (h∗)θ 1−τa

(1+τk)1−γ(1−α)

] 11−γ

∫B

[x (h∗)θ 1−τa

(1+τk)1−γ(1−α)

] 11−γ

dΨ

K ≡ $kK.

40

Aggregate production is then

Y =

∫B

ydΨ

=

∫B

(1− τa)x (h∗)θ(kαl1−α

)γdΨ

= TFP(KαL1−α)γ

where

TFP ≡∫B

(1− τa)x (h∗)θ$αγk $

(1−α)γl dΨ.

C Mapping Between Model and Data

The aggregate production function in the data is

Y = TFP(KαL1−α)γ ,

where L ≡ h`N is the total labor input, with h being human capital per worker, ` the

total number of workers per engaged person, and N the number of engaged persons (which

includes workers and the self-employed).

We proceed in a way analogous to the related literature employing decreasing returns to

scale technology (e.g. Buera and Shin, 2013) and abstract from scale effects. That is, we

treat the data as if N = 1 for both the U.S. and India, and rewrite the aggregate production

function in terms of (lowercase) variables per engaged person as

y = TFP(kα (h`)1−α)γ .

We rely on PWT8.1 data in order to back out TFP for the U.S. and India. We use data

for the year 2005 on current-year PPP-adjusted GDP per engaged person (variable CGDP o

divided by EMP ), capital stock per engaged person (CK/EMP ), and human capital stock

per engaged person (variable HC), together with our parameter values for α and γ. Human

capital stocks result from mapping average years of schooling from Barro and Lee (1993)

41

through an exponential human capital technology specification as in Caselli (2005), using

returns to schooling specific to each schooling level.

We assume that human capital per worker h, which we do not observe in PWT8.1, equals

human capital per engaged person. The total labor input h` is then computed by equating

` to one minus the rate of entrepreneurship from Table 4.

D Numerical Algorithm

We solve the model using value function iteration.

1. Discretization: Discretize ω into {ω0, . . . , ωNω}. We choose the upper bound and

lower bounds such that increasing them further apart has a negligible effect on the

solution.

The VAR(1) process for abilities is discretized into a Markov chain using the procedure

described in Tauchen and Hussey (1991).

2. Occupational choice and production: Solve for ω′ (q, h, x) given the current guess

for prices w and r.

(i) Compute the threshold level of saving q∗ (h, x).

(ii) Compute profits Π (q, h, x).

(iii) Compute next generation’s wealth ω′ (q, h, x).

3. Saving and education: Solve for the decision rules e (ω, z, x), s (ω, z, x), and

q (ω, z, x), given ω′ (q, h, x) from step 2, and given the current guess for prices.

(i) Guess value function V j (ω, z, x) at gridpoints.

(ii) Solve for the right-hand-side of the Bellman equation:

V j+1 (ω, z, x) = maxc,e,s,q

{u (c) + β

∑z′,x′

π (z′, x′|z, x)V j (ω′ (q, h, x) , z′, x′)

}

subject to (4)-(6).

42

First try an interior solution for q. If q ≥ −λφω then the solution has been

found. Otherwise set q = −λφω and find s and e subject to this constraint. V j

is approximated by a piecewise linear function for future wealth levels outside of

the grid.

(iii) Iterate until V j (ω, z, x) ≈ V j+1 (ω, z, x).

4. Invariant distribution: Approximate by simulating a large cross-section of N +

1 agents over a sufficiently large number of T periods. Decision rules are linearly

interpolated over a very fine grid.

5. Market clearing: Check whether the labor and capital markets clear. Compute

excess demand for labor and capital from the invariant distribution as:

EDL (w, r) =1

N

N+1∑n=2

[1n−1ln−1 + snl − (1− 1n−1)hn−1 − (1− sn)ψhn

]EDK (w, r) =

1

N

N+1∑n=2

[1n−1kn−1 −

qn1 + r

],

where 1n is an indicator which takes the value of 1 if household n chooses en-

trepreneurship and 0 otherwise. Iterate on market prices until EDL (w, r) ≈ 0 and

EDK (w, r) ≈ 0.

43

References

Amaral, P. S. and Quintin, E. (2010). Limited enforcement, financial intermediation,

and economic development: A quantitative assessment. International Economic Review,

51 (3), 785–811.

Atkeson, A. and Kehoe, P. (2005). Modeling and measuring organizational capital. Jour-

nal of Political Economy, 113, 1026–1053.

Barro, R. and Lee, J.-W. (1993). International comparisons of educational attainments.

Journal of Monetary Economics, 32, 363–94.

Barro, R. J. and Lee, J. W. (2013). A new data set of educational attainment in the

world, 1950–2010. Journal of Development Economics, 104 (C), 184–198.

Bartelsman, E., Haltiwanger, J. and Scarpetta, S. (2013). Cross-Country Differ-

ences in Productivity: The Role of Allocation and Selection. American Economic Review,

103 (1), 305–34.

Beck, T., Demirguc-Kunt, A. and Levine, R. (2000). A new database on financial

development and structure. World Bank Economic Review, 14, 597–605.

Bhattacharya, D., Guner, N. and Ventura, G. (2013). Distortions, endogenous man-

agerial skills and productivity differences. Review of Economic Dynamics, 16 (1), 11–25.

Bowles, S. and Gintis, H. (2002). The Inheritance of Inequality. Journal of Economic

Perspectives, 16 (3), 3–30.

Buera, F. J., Kaboski, J. P. and Shin, Y. (2011). Finance and development: A tale of

two sectors. American Economic Review, 101 (5), 1964–2002.

— and Shin, Y. (2013). Financial frictions and the persistence of history: A quantitative

exploration. Journal of Political Economy, 121 (2), 221 – 272.

Caselli, F. (2005). Accounting for cross-country income differences. In P. Aghion and

S. Durlauf (eds.), Handbook of Economic Growth, Handbook of Economic Growth, vol. 1,

9, Amsterdam, New York and Oxford: Elsevier Science, North Holland, pp. 679–741.

44

Castro, R., Clementi, G. L. and MacDonald, G. (2004). Investor protection, optimal

incentives, and economic growth. Quarterly Journal of Economics, 119 (3), 1131–1175.

—, — and — (2009). Legal institutions, sectoral heterogeneity, and economic development.

Review of Economic Studies, 76 (2), 529–561.

Clausen, A. and Strub, C. (2013). A general and intuitive envelope theorem, University

of Pensylvania.

Cordoba, J. C. and Ripoll, M. (2013). What explains schooling differences across coun-

tries? Journal of Monetary Economics, 60 (2), 184–202.

Dıaz-Gimenez, J., Glover, A. and Rıos-Rull, J.-V. (2011). Facts on the distributions

of earnings, income, and wealth in the United States: 2007 update. Quarterly Review.

Dunn, T. and Holtz-Eakin, D. (2000). Financial Capital, Human Capital, and the Tran-

sition to Self-Employment: Evidence from Intergenerational Links. Journal of Labor Eco-

nomics, 18 (2), 282–305.

Erosa, A. and Hidalgo-Cabrillana, A. (2008). On finance as a theory of TFP, cross-

industry productivity differences, and economic rents. International Economic Review,

49 (2), 437–473.

—, Koreshkova, T. and Restuccia, D. (2010). How important is human capital? a

quantitative theory assessment of world income inequality. Review of Economic Studies,

77 (4), 1421–1449.

Evans, D. and Jovanovic, B. (1989). An estimated model of entrepreneurial choice under

liquidity constraints. Journal of Political Economy, 97, 808–27.

Feenstra, R. C., Inklaar, R. and Timmer, M. P. (2013). The next generation of the

Penn World Table, available for download at www.ggdc.net/pwt.

Foster, L., Haltiwanger, J. and Syverson, C. (2008). Reallocation, firm turnover,

and efficiency: Selection on productivity or profitability? American Economic Review,

98 (1), 394–425.

45

Galor, O. and Zeira, J. (1993). Income distribution and macroeconomics. Review of

Economic Studies, 60 (1), 35–52.

Greenwood, J., Sanchez, J. and Wang, C. (2013). Quantifying the impact of financial

development on economic development. Review of Economic Dynamics, 16 (1), 194–215.

Hall, R. E. and Jones, C. I. (1999). Why do some countries produce so much more

output per worker than others? The Quarterly Journal of Economics, 114 (1), 83–116.

Henly, S. E. and Sanchez, J. M. (2009). The U.S. establishment-size distribution: secular

changes and sectoral decomposition. Economic Quarterly, 95 (4), 419–454.

Hsieh, C.-T. and Klenow, P. J. (2009). Misallocation and manufacturing TFP in China

and India. The Quarterly Journal of Economics, 124 (4), 1403–1448.

— and — (2010). Development accounting. American Economic Journal: Macroeconomics,

2 (1), 207–23.

International Monetary Fund (2006). Global Financial Stability Report: Market De-

velopments and Issues. Washington, DC: International Monetary Fund.

Kambourov, G. and Manovskii, I. (2009). Accounting for the changing life-cycle profile

of earnings, University of Toronto.

Kehoe, T. J. and Levine, D. K. (1993). Debt-constrained asset markets. Review of Eco-

nomic Studies, 60 (4), 865–888.

Klenow, P. J. and Rodrıguez-Clare, A. (1997). The neoclassical revival in growth eco-

nomics: Has it gone too far? In NBER Macroeconomics Annual 1997, vol. 12, Cambridge,

MA: MIT Press, pp. 73–103.

Levine, R. and Rubinstein, Y. (2015). Smart and Illicit: Who Becomes an Entrepreneur

and Do They Earn More? Tech. rep., University of California, Berkeley.

Lochner, L. J. and Monge-Naranjo, A. (2011). The Nature of Credit Constraints and

Human Capital. American Economic Review, 101 (6), 2487–2529.

46

Manuelli, R. E. and Seshadri, A. (2014). Human Capital and the Wealth of Nations.

American Economic Review, 104 (9), 2736–62.

Midrigan, V. and Xu, D. Y. (2014). Finance and Misallocation: Evidence from Plant-

Level Data. American Economic Review, 104 (2), 422–58.

Mitra, A. and Verick, S. (2013). Youth Employment and Unemployment: an Indian

Perspective. ILO Asia-Pacific Working Paper Series, International Labour Organization.

Moll, B. (2014). Productivity Losses from Financial Frictions: Can Self-Financing Undo

Capital Misallocation? American Economic Review, 104 (10), 3186–3221.

—, Townsend, R. M. and Zhorin, V. (2014). Economic development and the equilibrium

interaction of financial frictions, MIT.

Restuccia, D. and Rogerson, R. (2008). Policy distortions and aggregate productivity

with heterogeneous plants. Review of Economic Dynamics, 11 (4), 707–720.

Tauchen, G. and Hussey, R. (1991). Quadrature-Based Methods for Obtaining Approx-

imate Solutions to Nonlinear Asset Pricing Models. Econometrica, 59 (2), 371–96.

47